Financial terms of the deal announced Tuesday were not released.
Hayton, 22, was a restricted free agent and not initially listed on Arizona's roster for camp, which begins Thursday.
Hayton had 10 goals and 14 assists in 60 games with the Coyotes last season, all career highs.
Arizona drafted the player from Peterborough, Ontario, with the fifth overall pick of the 2018 NHL draft. He has 13 goals and 18 assists in 94 career games with the Coyotes.